We did the National Space. Centre in Leicester when doing that trip in reverse. I would recommend but maybe for older children. There was a website that listed things to visit along a route. I will try to find....

Clumber Park nr Retford is ace. It's a National Trust place about 2 minutes from the A1. We often stop there for lunch, you'll need to pay about a fiver for parking, but there is a nice national trust cafe and plenty of room for a 2 yr old to run around, chase ducks and there is a little play ground.

If it's really rainy, you could go into Retford itself, there is a big, good soft play and a few cafes etc

I have driven between London and Leeds via the M11 and A1 umpteen times, but didn't have children in tow. The halfway mark for me was roughly near Cambridge. I would think that your halfway point is likely to be Peterborough so would see if there is anywhere near there to visit.